Entropy and the Closed System

So in my physics textbook, the 2nd law of thermodynamics stated in terms of entropy reads "the entropy of a closed system can never decrease." Now, shouldn't it indicate the entropy of an isolated system can never decrease. All other sources I've looked at note an isolated system, as well. Any clarification would help.

Your book appears to be using non-standard definitions of isolated and closed systems. An isolated system is completely isolated from the external environment. Another way to look at it: There is no external environment for an isolated system. The external environment starts coming into play with closed systems. A closed system can exchange energy but not matter with the external environment. The entropy of a closed system *can* decrease. This is how air conditioners work.

So in my physics textbook, the 2nd law of thermodynamics stated in terms of entropy reads "the entropy of a closed system can never decrease." Now, shouldn't it indicate the entropy of an isolated system can never decrease. All other sources I've looked at note an isolated system, as well. Any clarification would help.

An isolated system is a hypothetical system which cannot exchange matter or energy with any other system and is likewise isolated from any environment other than the system itself. They are idealized models and are not considered to exist in nature.

A closed system cannot exchange matter with other systems or the environment, but can and does exchange energy.

I think the idea is that the collection of all closed systems includes systems such as "the whole universe". "Isolated system" could be problematic here, because it could oxymoronically imply the existence of dynamical stuff outside of "the whole universe". The associated problem for "closed systems" (namely, that there exists matter beyond a "closed" spin ensemble) can be avoided by defining a closed system to be one where there are no interactions with stuff that could potentially be outside. The problematic aspect of the definition here is that "interactions" are often not discussed in the most general thermodynamic context. Thermodynamics is such a phenomenological subject that precise definitions aren't especially important, however: what is most important is that the physical picture for a particular model is clear. You are essentially free to use whatever physical justification you can think of, as long as it is consistent with the model in question. If you introduce extra detail in your thought experiment, then you can always suggest corrections to the model that is being described that include the effects that you are imagining. This is one of the properties of thermodynamics (more importantly/recently statistical mechanics) that makes the field so interesting: you can always return to basic problems that you thought about years beforehand and find something new and interesting to say about them.

EDIT: As mentioned in other replies, the definition of a closed system is different from that for an isolated system (see http://en.wikipedia.org/wiki/Closed_system). Thus, the entropy for a closed system can decrease as when heat is exchanged between a thermal bath and a system (both the heat bath and the system are closed, but not isolated: here the joint system consisting of both the heat bath and the system is isolated).

I understand the respective definitions of a closed and isolated system. The textbook I use doesn't seem to sway from the standard definition. The definition of a closed system as stated in earlier chapters is
'' a system into or out of which thermal energy can be transferred but from which no constituents can escape and to which no additional constituents are added."

One example in the text states, water is placed into a freezer, and enough heat is removed from the water to freeze it completely to ice at a temperature of 0 °C. Then the problem asks how much does the entropy of the water-ice system change during the freezing process? We obtain an entropy change of -1830 J/K. Now clearly, the entropy of the water-ice system has decreased. The textbook then indicates the water-ice system is not a closed system. The text then states the freezer used energy to remove heat from the water to freeze it and exhausted the heat into the local environment. So wouldn't this still be considered a closed system, according to the definition I outlined above, as only thermal energy has been transferred????

Wouldn't it make more sense to consider the freezer and water-ice system to be collectively thought of as a isolated system, and individually as closed systems. Then the overall entropy of the isolated system increases (in accordance with the second law) more than the entropy of the water-ice system decreases.

I forgot to mention earlier, the textbook I'm referring to is University physics with modern physics by Bauer and Westfall.

According to the above definitions of closed and isolated systems, the freezer+water+ice system may not be closed, if the freezer performs work in order to transfer internal energy from the water to the environment (if you have not done so, I would recommend reading about the thermodynamic description of how refrigerators work). In case the freezer is simply a large cold bath, then the freezer+water+ice system is closed. If the freezer+water+ice is not coupled to the environment, then it is also isolated. Individually the ice system and the water system are not closed, because water molecules are free to transition between the solid and liquid phases. The ice+water system is closed (to a decent approximation), because we are assuming that the water molecules do not exist in the gas phase (alternatively, we are grouping the gas and liquid phases together in our theoretical description, or in our parameters obtained from fitting our model to data).